[BZOJ3533]向量集

#include<stdio.h>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long ll;
struct point{
	int x,y;
	point(int a=0,int b=0){
		x=a;
		y=b;
	}
}p[400010],stack[400010];
ll operator*(point&a,point&b){
	return a.x*(ll)b.x+a.y*(ll)b.y;
}
ll operator/(point a,point b){
	return a.x*(ll)b.y-a.y*(ll)b.x;
}
point operator-(point&a,point&b){
	return point(a.x-b.x,a.y-b.y);
}
typedef vector<point> vp;
vp up[1600010],down[1600010];
ll lastans;
int l[400010],r[400010],top;
bool op[400010];
void decode(int&x){
	x^=lastans&0x7fffffff;
}
bool cmp1(point a,point b){
	if(a.x==b.x)return a.y<b.y;
	return a.x<b.x;
}
void getup(vp&v){
	if(v.size()==0)return;
	sort(v.begin(),v.end(),cmp1);
	top=1;
	stack[0]=v[0];
	int i;
	for(i=1;i<v.size();i++){
		while(top>1&&(stack[top-1]-stack[top-2])/(v[i]-stack[top-1])>=0)top--;
		stack[top]=v[i];
		top++;
	}
	v.clear();
	for(i=0;i<top;i++)v.push_back(stack[i]);
}
bool cmp2(point a,point b){
	if(a.x==b.x)return a.y>b.y;
	return a.x<b.x;
}
void getdown(vp&v){
	if(v.size()==0)return;
	sort(v.begin(),v.end(),cmp2);
	top=1;
	stack[0]=v[0];
	int i;
	for(i=1;i<v.size();i++){
		while(top>1&&(stack[top-1]-stack[top-2])/(v[i]-stack[top-1])<=0)top--;
		stack[top]=v[i];
		top++;
	}
	v.clear();
	for(i=0;i<top;i++)v.push_back(stack[i]);
}
void modify(int pos,point&p,int l,int r,int x){
	up[x].push_back(p);
	down[x].push_back(p);
	if(pos==r){
		getup(up[x]);
		getdown(down[x]);
	}
	if(l==r)return;
	int mid=(l+r)>>1;
	if(pos<=mid)
		modify(pos,p,l,mid,x<<1);
	else
		modify(pos,p,mid+1,r,x<<1|1);
}
ll solve(int x,point&p){
	int i,l,r,m1,m2;
	ll ans=-9223372036854775807ll;
	if(p.y>0){
		l=0;
		r=up[x].size()-1;
		while(r-l>2){
			m1=((l<<1)+r)/3;
			m2=(l+(r<<1))/3;
			if(up[x][m1]*p<up[x][m2]*p)
				l=m1;
			else
				r=m2;
		}
		for(i=l;i<=r;i++)ans=max(ans,up[x][i]*p);
	}else{
		l=0;
		r=down[x].size()-1;
		while(r-l>2){
			m1=((l<<1)+r)/3;
			m2=(l+(r<<1))/3;
			if(down[x][m1]*p<down[x][m2]*p)
				l=m1;
			else
				r=m2;
		}
		for(i=l;i<=r;i++)ans=max(ans,down[x][i]*p);
	}
	return ans;
}
ll query(int L,int R,point&p,int l,int r,int x){
	if(L<=l&&r<=R)return solve(x,p);
	int mid=(l+r)>>1;
	ll ans=-9223372036854775807ll;
	if(L<=mid)ans=max(ans,query(L,R,p,l,mid,x<<1));
	if(mid<R)ans=max(ans,query(L,R,p,mid+1,r,x<<1|1));
	return ans;
}
int main(){
	int n,m,i,now;
	char s[5];
	bool sec=0;
	scanf("%d%s",&m,s);
	if(s[0]!=‘E‘)sec=1;
	n=0;
	for(i=1;i<=m;i++){
		scanf("%s%d%d",s,&p[i].x,&p[i].y);
		op[i]=s[0]==‘A‘;
		if(op[i])
			n++;
		else
			scanf("%d%d",l+i,r+i);
	}
	now=0;
	for(i=1;i<=m;i++){
		if(sec){
			decode(p[i].x);
			decode(p[i].y);
		}
		if(op[i]){
			now++;
			modify(now,p[i],1,n,1);
		}else{
			if(sec){
				decode(l[i]);
				decode(r[i]);
			}
			printf("%lld\n",lastans=query(l[i],r[i],p[i],1,n,1));
		}
	}
}